Fundamental finite key limits for one-way information reconciliation in quantum key distribution

Marco Tomamichel*, Jesus Martinez-Mateo, Christoph Pacher, David Elkouss

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)


The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during information reconciliation is not generally valid. We propose an improved approximation that takes into account finite key effects and numerically test it against codes for two probability distributions, that we call binary–binary and binary–Gaussian, that typically appear in quantum key distribution protocols.

Original languageEnglish
Article number280
Number of pages23
JournalQuantum Information Processing
Issue number11
Publication statusPublished - 1 Nov 2017


  • Finite length
  • Low-density parity-check codes
  • Quantum key distribution


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